Condition numbers for the <i>K</i>-weighted pseudoinverse and their statistical estimation

Abstract

The explicit expressions of normwise, mixed and componentwise condition numbers for the K-weighted pseudoinverse LK† are first presented. With the intermediate result, i.e. the derivative of LK†, we can recover the explicit expressions of condition numbers for solution of least squares problem with equality constraint. Then, we investigate the statistical estimation of condition numbers of LK† using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, numerical examples are provided to illustrate these results.